相关论文: Direct and inverse abstract Cauchy problems with f…
We study Cauchy problems of fractional differential equations in both space and time variables by expressing the solution in terms of ``stochastic composition" of the solutions to two simpler problems. These Cauchy sub-problems respectively…
We introduce a class of fractional Dirac type operators with time variable coefficients by means of a Witt basis, the Djrbashian-Caputo fractional derivative and the fractional Laplacian, both operators defined with respect to some given…
Problems of the numerical solution of the Cauchy problem for a first-order differential-operator equation are discussed. A fundamental feature of the problem under study is that the equation includes a fractional power of the self-adjoint…
In this work, we study the inverse problem of determining a potential coefficient in an abstract wave equation that includes a lower-order term. The equation incorporates a time-fractional derivative in the Caputo sense, as well as a…
Fractional Cauchy problems replace the usual first-order time derivative by a fractional derivative. This paper develops classical solutions and stochastic analogues for fractional Cauchy problems in a bounded domain $D\subset\mathbb{R}^d$…
We study the uncoupled space-time fractional operators involving time-dependent coefficients and formulate the corresponding inverse problems. Our goal is to determine the variable coefficients from the exterior partial measurements of the…
In this work I consider the abstract Cauchy problems with Caputo fractional time derivative of order $\alpha\in(0,1]$, and discuss the continuity of the respective solutions regarding the parameter $\alpha$. I also present a study about the…
In this paper we explore the theory of fractional powers of non-negative (and not necessarily self-adjoint) operators and its amazing relationship with the Chebyshev polynomials of the second kind to obtain results of existence, regularity…
In this paper we explore the theory of fractional powers of maximal accretive operators to obtain results of existence, regularity and behavior asymptotic of solutions for linear abstract evolution equations of third order in time.
A boundary value problem for a fractional power of the second-order elliptic operator is considered. It is solved numerically using a time-dependent problem for a pseudo-parabolic equation. For the auxiliary Cauchy problem, the standard…
We focus on eventually non-linear abstract Cauchy problems with a generalized fractional derivative in time. First we prove a local existence and uniqueness result, then we focus on a generalized Gr\"onwall inequality. Before addressing the…
In this paper, we investigate the direct and linear inverse problems of identifying time-dependent and time-independent source terms in a time-fractional diffusion-wave equation, using measured data at an interior point of the time…
We investigate the variable-exponent Abel integral equations and corresponding fractional Cauchy problems. The main contributions of the work are enumerated as follows: (i) We develop an approximate inversion technique for variable-exponent…
We present an exponentially convergent numerical method to approximate the solution of the Cauchy problem for the inhomogeneous fractional differential equation with an unbounded operator coefficient and Caputo fractional derivative in…
We consider the Cauchy problem for stochastic fractional evolution equations with Caputo time fractional derivative of order $1<\alpha<2$ and space variable coefficients on an unbounded domain. The space derivatives that appear in the…
In this work, we investigate a unique solvability of a direct and inverse source problem for a time-fractional partial differential equation with the Caputo and Bessel operators. Using spectral expansion method, we give explicit forms of…
In this paper, we define an operator function as a series of operators corresponding to the Taylor series representing the function of the complex variable. In previous papers, we considered the case when a function has a decomposition in…
We consider a time-independent variable coefficients fractional porous medium equation and formulate an associated inverse problem. We determine both the conductivity and the absorption coefficient from exterior partial measurements of the…
In this paper, we investigate direct and inverse problems for the time-fractional heat equation with a time-dependent leading coefficient for positive operators. First, we consider the direct problem, and the unique existence of the…
The purpose of this paper is to establish the solvability results to direct and inverse problems for time-fractional pseudo-parabolic equations with the self-adjoint operators. We are especially interested in proving existence and…